<p>Hyperelastic constitutive models for rubber-like materials (RLMs) have been widely used to predict nonlinear deformation behaviors; however, selecting a model that balances mathematical flexibility with physical consistency remains challenging. In this study, a generalized phenomenological formulation defined as a convex (linear) combination of the Ogden and polynomial strain-energy functions is proposed. The proposed framework incorporates both principal stretches and strain invariants and can reproduce classical forms (e.g., Mooney–Rivlin and Yeoh from the polynomial branch, and Ogden-type responses) by selecting the polynomial indices and the weighting coefficient. A key advantage of the proposed formulation is that material stability is discussed in the sense of Drucker-type stability (non-negative incremental work). In particular, energy convexity— with polyconvexity as a standard sufficient condition—provides a rigorous route to stable behavior, and this property is preserved under convex combinations. The model was implemented via a Vectorized User Material (VUMAT) subroutine for ABAQUS/Explicit and validated using Treloar’s classic data and experimental results from three deformation modes (uniaxial tension, equi-biaxial tension, and pure shear). Beyond conventional stress–strain fitting, the proposed model demonstrates improved derivative fidelity, capturing slope transitions and tangent stiffness evolution across strain regimes. Practical validation is further conducted through a G-bush component tension test. By calibrating the material response to the dominant operating strain window of the component (approximately 50–70% strain), the proposed model yields improved component-level predictions compared with conventional Ogden and Yeoh models. These results suggest that the blended potential offers a numerically stable framework in the tested configurations for high-fidelity simulation of industrial rubber components.</p>